An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry-Summary of the Formulation-
INFN Sezione di Torino, and Dipartimento di Fisica Teorica, Universita di Torino I-10125 Torino, Italy
2 Department of Physics, Hokkaido University Sapporo, 060-0810 Japan
3 Department of Human Science, Obihiro University of Agriculture and Veterinary Medicine Obihiro, 080-8555 Japan
Published online: 26 March 2018
We propose a lattice field theory formulation which overcomes some fundamental diffculties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the lattice, the star product, and the chiral fermion species doublers degrees of freedom can be avoided consistently. This framework is general enough to formulate non-supersymmetric lattice field theory without chiral fermion problem. This lattice formulation has a nonlocal nature and is essentially equivalent to the corresponding continuum theory. We can show that the locality of the star product is recovered exponentially in the continuum limit. Possible regularization procedures are proposed.The associativity of the product and the lattice translational invariance of the formulation will be discussed.
© The Authors, published by EDP Sciences, 2018
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